| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
| 15.3.871...000.1 |
$x^{15} - 30 x^{10} - 3708 x^{5} - 2$ |
$15$ |
[3,6] |
$2^{14}\cdot 3^{20}\cdot 5^{16}$ |
$3$ |
$45.9929225331$ |
$52.59427916529308$ |
|
|
? |
$C_{15} : C_4$ (as 15T6) |
trivial |
$2$ |
$8$ |
$11609195.2059$ |
| 15.15.897...000.1 |
$x^{15} - 3 x^{14} - 37 x^{13} + 91 x^{12} + 483 x^{11} - 829 x^{10} - 2993 x^{9} + 2941 x^{8} + 9853 x^{7} - 3339 x^{6} - 16675 x^{5} - 2811 x^{4} + 11401 x^{3} + 6327 x^{2} - 59 x - 401$ |
$15$ |
[15,0] |
$2^{14}\cdot 3^{6}\cdot 5^{6}\cdot 37^{10}$ |
$4$ |
$62.6420048698$ |
$110.95790593274286$ |
|
|
? |
$C_{15} : C_4$ (as 15T6) |
trivial |
$2$ |
$14$ |
$1159585432.29$ |
| 15.15.162...296.1 |
$x^{15} - x^{14} - 43 x^{13} + 95 x^{12} + 384 x^{11} - 1078 x^{10} - 750 x^{9} + 3194 x^{8} + 2 x^{7} - 3384 x^{6} + 816 x^{5} + 1106 x^{4} - 303 x^{3} - 77 x^{2} + 5 x + 1$ |
$15$ |
[15,0] |
$2^{12}\cdot 229^{10}$ |
$2$ |
$65.1699895602$ |
$117.73527632186602$ |
|
|
|
$C_{15} : C_4$ (as 15T6) |
trivial |
$2$ |
$14$ |
$3158277360.78$ |
| 15.3.503...000.1 |
$x^{15} - 506 x^{10} - 36760 x^{5} + 972$ |
$15$ |
[3,6] |
$2^{14}\cdot 5^{16}\cdot 17^{10}$ |
$3$ |
$70.279492194$ |
$80.36669618858696$ |
|
|
? |
$C_{15} : C_4$ (as 15T6) |
trivial |
$2$ |
$8$ |
$294344339.262$ |
